Persistence modules, symplectic Banach–Mazur distance and Riemannian metrics

We use persistence modules and their corresponding barcodes to quantitatively distinguish between different fiberwise star-shaped domains in the cotangent bundle of a fixed manifold. The distance two is measured by nonlinear version classical Banach–Mazur distance, called symplectic denoted [Formula: see text]. relevant come from filtered homology are stable with respect Our main focus on space unit codisc bundles orientable surfaces positive genus, equipped Riemannian metrics. consider some questions about large-scale geometry this particular we give construction quasi-isometric embedding text] into for all On other hand, case text], can show that metric has infinite diameter. Finally, discuss existence closed geodesics whose energies be controlled.